Spline curves

• The term spline curve now refers to any composite curve formed with polynomial sections satisfying any specified continuity conditions at the boundary of the pieces.

• A spline surface can be described with two sets of spline curves.

• Splines are used to design curve and surface shapes, to digitize drawings, and to specify animation paths for the objects or the camera position in a scene.

Interpolation and approximation splines

• We specify a spline curve by giving a set of coordinate positions, called control points

• In Figure 1, the resulting curve is said to interpolate the set of control points.

• In Figure 2, the resulting curve is said to approximate the set of control points

Bézier Spline Curves

• This spline approximation method was developed by the French engineer Pierre Bézier for use in the design of Renault automobile bodies.

• Bézier splines have a number of properties that make them highly useful and convenient for curve and surface design.

• A Bézier curve section can be fitted to any number of control points, although some graphic packages limit the number of control points to four.

• The degree of the Bézier polynomial is determined by the number of control points to be approximated and their relative position.

Challenge: Dynamic Bézier Curve-Generating

OpenGL complete sample code / Processing

• Design a program that will dynamically draw a bézier curve as the control points are being defined with mouse clicks
• First and second clicks will define the first and final control points
• Third and fourth clicks will define 2 dynamic control points
• Dynamic control points can be moved with the mouse (click and drag)

More Spline Curve Algorithms

• B-Spline Curves
• Beta-Spline Curves
• Rational Splines

Check chapter 13 of the book

What's next

Surfaces

Views

Projections

Resources and Credits

This material is genereated thanks to some extracts from following resources:

• Computer Graphics with OpenGL (Chapter ) by Donald D. Hearn/M. Pauline Baker, Warren Carithers, 4th Edition

Thanks

• Obed N Muñoz Reynoso
  • Cloud Software Engineer
  • obed.n.munoz@gmail | tec | intel.com